Electromagnetic resolver



Aug. 26, 1952 D. HERR 2,608,682

ELECTROMAGNETIC RESOLVER Filed NOV. l5, 1949 Aug. 26, 1952 15. L. HERR 2,608,6821

1N VEN TOR.

Aug. 26, 1952 D. L. HERR 2,608,682

ELECTROMAGNETIC RESOLVER Filed Nov. 15, 1949 7 Sheets-Sheet 3 :I Y INVENTOR.

Aug. 26, 1952 D. HERR v 2,608,682

' ELECTROMAGNETIC RESOLVER Filed Nov, 15. 1949 7' sheets-sheet 4 i da y JNVENTOR.

Aug. 26, 1952 D. l.. HERR 2,608,682

ELECTROMAGNETIC RESOLVER Y Filed Nov. 15, 1949 7 Sheets-Sheet 5 BY MMI/gn... lA/

Aug 26, 1952 D. L. HERR 2,608,682

ELECTROMAGNETIC RESOLVER Filed Nov. 15, 1949 7 sheets-sheet e JNVENTOR. 7o/maal. HCF/PP www @m W www `terial; and air 'gap employed.

l tion and suppression Patented Aug. 26, 1952 ELECTROMAGNETIC RESOLVER Donald L. Herr, New York, N. Y., `ass'gnor to Reeves Instrument Corporation, New York,. Y N. Y., a corporation of New York Application November 15, 1949, YSerial No. 127,438

The present invention relates toimprovements in electromagnetic devices and relates in particular to an alternating current, electromagnetic resolver.

An Vobject of the present invention is to provide an electromagnetic resolver which will have high precision and accuracy. ,at a plurality of useful carrier frequencies suchas 60, 400 and 1,000 cycles per second. Another object ofthe invention is to provide a resolver that may be manuflactured in quantity with the assurance that the desired standard of precision and accuracy will be present in eachinstrument. By achieving suchrobjectives, the present invention materially reduces thecost of such instruments and also provides a resolver of greater precision and accuracy than those heretofore available.

Generally speaking, electromagnetic resolvers thatlare known to the `art and available commercially are not so universal. in their carrier frequency application and .because of various shortcomingsintheir construction they are eX- pensive instruments to manufacture. One reason for this is that in the `manufacture of such resolvers, it is` necessary to match the windings by hand in order to obtain high precision and accuracy. However, even thematchingof windings by hand'do'es not make it possibleto obtain high precision and. accuracy lin all resolvers and a large percentagof suchresolvers are not suitable for uses wherehigli standardsH must be met.

In accordance f `witljr the present inventionan electromagneticrsolver isfprovided that has the folowing features''f (a)` Magnetic, mechanical, and electrical equivalence of both statorwindings, and the same kind vof equivalence of both rotor windings.

(b) The ability to `develop the maximum ratio of reactance `to resistancein each stator Winding consistentv with the dimensions, magnetic ma- (c) `Identical space harmonic content, time harmonic content, land `identical phase angles (time andspacellas well as identical space harmonic generation, rejection and suppression patterns, for both stator windings. r

(d) Identical space harmonic induction, rej ecpatterns, for both rotor windings. i. l C L l (e) Slot rand conductor distributions for the stator and rotor enabling a desired space harmonic pattern and resolver accuracy to Vbe achieved. A Y

(j) The establishing of optimum dimensions of stator, rotor, and air gap for which, if suitable magnetic material is used, the resolver be haves as if the total reluctance of any flux path, is essentially only that of the air gap.

(g) MinimumV stator and rotor zeroespacing error.V

22 claims. (ol. 336-420) (h) Minimum stator and rotor space inter-axis error. v

(i) Minimum quadrature time-axis component.

Further objects and advantages ofthe invention will be'apparent and best understood from the following description and the accompanying drawings ln which: E

Fig. 1 is a side view in section of a resolver embodying the present invention;

Fig. 2 is an end view of the resolver illustratedV in Fig. 1;

Fig. 3 is an end View of the resolver illustrated in Fig. 1 with the cover removed; Y

Fig. 4 is a planview of a stator lamination for a resolver such as is illustrated in Fig. 1A;

Fig. 5 is a plan view of a rotor lamination for a resolver such as is illustrated in Fig.` 1; l

Fig. 6 -illustrates schematically `the conductor' Fig. 9 is a fragmentary View in section taken along the line 99Vof Fig. 3.

Fig. 10 is a schematic diagram illustrating one function of a resolver; and A Y Fig. 11 is a schematic diagram illustratingv another typical function of a resolver; and

Fig. 12 is an equation for determining the distribution of conductors in .the stator and rotor of a resolver embodying the inventionwith an explanation of the Vsymbols used therein.

In general, an alternating-current electromagnetic resolver hasa stator and a rotor which.

have salient poles with an appropriate degree'of skewing and discretely distributed windings Si and S2 on the stator andwindings R1 :and R2 on the rotor. "The stator windings-"S1 and Sz are matched and are mechanically'90 Adegrees apart. The rotor windingsRi and Raalte also vmatched and are mechanically 90 degrees apart. Functions which such analternating current' electromagnetic resolverlm'ay perform are illustrated in Figs. 10 and 11.

When, as illustrated in Fig. 10, A. C. voltagesV proportional to En and ,E szlare applied asinputs to the stator windingsSi vand-Sz respectively',` the -resolver rotor will be rotated to and indicate an angle of rotation a=tan1 Esa/Esi by Connecting the rotor winding R1 to a nullingf device and a voltage proportional to' A Y metry mechanically 90 degrees apart.

will be obtained as the output of the rotor winding R2. As illustrated in Fig. 11 when a voltage proportional to Esi is applied as the resolver inputY to the stator Winding S1 Iand the. rotor is rotated toan :angle a, voltages proportional to Y and lET1=E82 sin a areobtained as outputs fromthe rotor win-dings R1 and R2, respectively.

The two distributed statorwindingsr S1 and' Sz occupy the same magnetic structure in the sta-tor with their axes of electrical Asymmetry mechanically 90 degrees apart. Each ofthe stator wind-A ings S1 'and S2 develops an A. C. flux-density dis- Ytribut'io'rrin'the stator-rotor airgap (in Fig'S) which is ideally sinusoidal or cosinusoidal in the angle of position on'the stator periphery, lfund-avment-al in `the space-period of the air-gap circumtor windings, a' net A; C. voltagewhich is ideally sinusoidal or co-sinusoidal in the :angle of rotor rotation With respect to the stato-r, fundamental in the space-period of theair-g'ap circumference :and proportional to the A. C.fvoltage applied to either stator Winding.

Such an instrument may be used for solving trigonometric and analytical problems such as the rotation of coordinates. lthe transformation of polar coordinates to rectangular coordinates, and vice-versa, :and the resolution :and :addition of vectors.l "Such an instrument may also be used for high' precision jdata `transmission .as it may be more-accurate than a synchrolandxmay eliminate thelnecessity flor double sets of transmitters and receivers. Y n Referring to Fig.v`1,there is a resolver I0. The resolver I has a statorI'I anda rotor I2 both of which are made of laminated magnetic'material. Such magnetic material is preferablyfof the high permeability low core-loss type as,` for example, those materials whosecomposition i's'4'7 to 5Il% nickel and approximately 50%pure iron, app-ropriately hydrogen annealed. A secondary material is electrical silicon 'steelcommonly known as transformer-C grad-e. T-he rotor and vstator laminations should be'.0'1,4 of 'an inch or less in thickness.A By making the laminations of such thickness a suicien-tly great ratio'of storedmagnetic energy per unit volume to dissipative energy per unit volunreof the magnetic structure is obtained that permitsthe resolver tozfun'ction with the desired degree of "accuracy over awide range off carrier frequencies.

lThe stator.V I'I is located inside of atubular or Y cylindrical housing. 'Oneendof thehousing is opento. receive thestator and thestator is positioned 'Within the housingby' a magnetic shield I'4 and an end be1l'I5 that also serves as a mag-V netic shield anda bearing support. The housing IB'a'ndn'the end bell I5 areV also made o f metal or other material -tliatwill serve as a magnetic shieldV for the st-atorandrotor. The rotor I2 is rotatably supported inside of the stator lI3 on a shaftIS. j .i t

The rotor shaft I6 Aextends through .the closed end of the housing I3 and is journalled in a bearing I1 carried by the housing. The other end of the shaft 1s extends through the end bien is and journalled in a bearing I8 carried by the end bell. This end oi the rotorI .shaft [5f-carries a series of contact rings I9 that areinsulated from each other .byspacers 2D.' TThe'win'dings R1 and .Rx of the rotor are connected to the Contact rings I9 by conductors 2| that run through the shaft I6. A spring brush 22 engages with each of the contact rings 19 and connects them to xed contact pins 23 `that are. supportedin conductor bars The 'conductor' ybars 214 are Wedge-shaped :and

are removably supported in spaced relation to Y each other in a brush mounting ring 25 of insulating material that is secured to the end bell I 5 by screws 25. The conductor bars 24 are held in place in the brush-mounting ring 25 bya sleeve` or collar 21 ofinsulatingmaterial that ts over:

the ring -25.' As shown best in'FigyS, the statorv windings Si 'and S2 are connected to Contact pins 28 by conductors y'29 that pass-through aligned openings |30 and BI inthe end bell and the ring' 25, respectively. Th'e'contact pins 28 are also" supported by the riiigf25. 'i l Y The contact pins 23'forthe rotor windings Ri andI R2 andthe contact pins 28 for the stator windings Si and S2 extend through a cover disc 32 of insulating material that encloses the open end of the housing I3. The cover disc 32 is se'- cured tothe end bell I5by screws 33 and it,v in` v turn, secures ythe lsleevev 21 and the conductor bars 24 against lengthwise movement relative f to the brush-mounting ring 25. This assembly consisting of the end bell I5, the contact pins 23 andf28 and the brushes 22 is secured in'posi` tionwithin the open end of the housing I3 by aj'- spanner nut y34thatengages with threads'bon the inside of the housingjl3. The Spanner nuty 3d* is rotatably carriedbetween the brush-mounting' ring 25 andthe end' bell I 5 and may be threaded in place prior to the installation of the sleeve"v 2I` and the cover disc'32.

Appropriate connections may lloelrnade tothe" end -of the shaft lernst-'extends beyond the' housing -I3 sol that; the rotor maybe turned 'inj angularirelation tothe's'tator as desired. y The housing I v3jalsoy carries an-annular gear isector" 351cmitstouter'surfacel "The fg'ear vsector 35 eig-.

tends for approximately 40 around the fupper right hand` quadrant of the housingxand'provides means for rotating thehousing and'l the y'stator for zeroing the resolver when the rotor is held stationary.

the illustrated embodiment, has twelvebars is and a likenumberof conductor slots 4i in which the conductors drofthe ArotorWindings'lti and Rfareplad ,e ,s

Inbrder to obtain identical Adistribution ofthe stator windingsSi and S2 and of the rotor wind# ings Riand Rein-the conductor-'slots 38 and 4I of the stator fIjIandv-'ther'otor I2,1respectively,` With the axes-'of electrical-symmetry of said Wl'nd'V-'f ings being mechanically degrees apart, 'the4 number of bars andiconductor slots in the stator II and the rotor I2 are integral multiples? of'V four. Y In addition,` the number of bars for the stator II shouldA preferably be four or more n greater than the number of barsfor the rotor I 2*'V with a minimum' number ofv twelve bars vfor the number of eight `bars cemented together with suitable-adhesives with the successive individual laminations being insulated from each otherand'4 progressively offset angularly with respect to each other to minimize any residual effects of possible magnetic orientation in the material itself.- The stacked laminations forming the stator and rotor pref-` erably are approximately one and one half (l1/2) inches inlength and the rotor -preferably is approximately one inch in diameter. 1 i I After the laminations are stacked and cemented together, they arethen baked tobond the adhesive and after bakingthe inner and outer major surfaces of the stator II and the outer surface Aof. the rotor I2` may beground to a final commonconcentricity, smoothness and appropriate diameters. Such 4grinding also renders the surfaces of the stator II and the rotor l2 Vmore stable magnetically than otherwise so that accidental striking or jarring of these surfaceslwill not distort the magnetic-pattern pro--` duced. l The air gap @between the stator and rotor `should preferably be not greater than .00625 of an inch.

Also, in stacking the rotor laminations 39, they are skewed so that the bars 24 follow a helical path with a pitch equal to the distance of one pole in the length of the rotor. This is designated as a per unit skewness K of unity. `For purposesof simplicity ofdiscussiom all ,skewness will be assumed to be ,wholly in the rotor.; However, it will be understood that the skewness may be partially or entirelyin the stator Il' soflong as the total skewness results in a degree of skewness that is equivalent to a skewnessv of unity in the rotor. f

l'I'he'purpose of skewing the bars of either the rotor or stator orbothin thisV manner is to -reduce the amplitude of those unwanted space harmonics which are both generated by the stator windings and are capable of being induced in the rotor windings. For example, an unskewed twenty bar stator and an unskewed twelve bar rotor are a combination that will completely suppress'all space harmonicspbegin- "Al'sfwhile in the illustrated 'embodiment of` the invention, the rotor I2 is described and shown as the rotatable member, it will be understood that in any application or use, either the stator Il or the rotor I2 may be the rotatable member and the other fixed member.

Ajlso, in order to obtain the optimurriaccuracy` and precision, the effective magnetic diameters of the stator Il and the rotor I2 should be in the proportion of 3 to l. For example, as illus-l trated infFig. 8, the eifectivelinagnetic diameter ofthe rotor I2 'approaches one-third the effective magnetic' diameter of the'stator Il.` i

The manner in which-.thelconductorscs and dr ofone of the stator windings -Si (or S2) and the conductors `of vone of Vtherotor'windings R1 (or Rz) Vare distributed inthe-conductor slots 38 and 4I of the statorfand rotor,` respectively, to obtain symmetrical distribution is schematically illus-` trated in Figsf and 'with'the conductorsfor the stator androtor windingsllbeingV identiedby the :reference character' ci'ec'sland x11-d3, respectively. AThev directionin'which currentflows inf theconductorsfcicsi of the. statorwindin'g and in theifconduct'ors Z1-ds ofthe rotor'winding is indicated vby the arrowsrin Figs. G'fandfl, `respectively, and `this illustrates one way' iriwhich these` ,windings may be connectedtoobtain the desired electrical characteristics.`

The second windingfon the stator and rotor,

respectively.A 4issimilarly distributed and con-v nected Vexceptv that the lelectrical axes' ofl these windings Vare displaced `mechanicall'yfby 90 degrees from the windings illustrated in Figs. 6 and 7. In Fig. 8,.connecti'on ofthe conductorsof the stator windings Siand Si and of the rotor windings R1 and Rz are shown schematicallywith the connections for the conductors of the stator winding S1- and the rotor winding R1 being represented by fulll lines and the connections for the stator windingSz a-nd'the .rotor winding R2 being representedby the brokenlines.v Aswill be seen from Fig. 8 thefstatorwindings -Si and Sz are identical to eachother andltheir axes of electrical symmetry are mechanically degrees apart. The rotor windings R1 and Rz are also identical to each other and their .axes of electrical symmetry are mechanically 9i) degrees apart. In this figure,` the axes of electrical symmetry are indicated by the line A-A for the stator winding Si; by the line B-"B for the stator Winding S2; thelinc C--C for the rotor winding R1; and by the line D-D for the rotor winding Rz. The symbol ps indicates the stator diameter; the symbol pr indicates the rotor diameter; the symbol a indicates `the anglethrough which the rotor has been rotated with=respecttcthe stator; the symbol n indicates rarpo'siticn'in-Y the rotor periphery with respect to the 'reference rotor co- .ordinate and the symbol' o 4indicates a corresponding position in the stator periphery with respect to the reference stator coordinate.

Each ofthe stator windings S1 and Sz is designed toy develop an A. C. flux-density distribution `in the stator-rotor air-gap which is (ideally) sinusiodal or (so-sinusoidal in the angle of `position on the stator periphery, fundamental in the space-periodrof the air-gap-circumference and proportional to theA.` C. voltage applied Ato' the. stator winding. The conductor distribution of the windings is so chosen as to minimize or The'equation set forth in Fig. 12 represents the stator to rotor transfer-function of an idealized 4.111 an electromagnetic `instrument of: the character' described. the/combination as' defined in claim l whereinthe. ratio .of .the'eiective magnetic diameterof Vthe statorto the effective mag- ,neticdiamete'r zot. the 'rotor is' three to one.

5, In'. an. valternatingecurre'nt electromagnetic .resolver,.;the combination including a stator consisting of laminations. of a hig'hpermeability low core-loss magnetic material. said laminations being insulated from each other with each of .said laminations `bei-ng kof a. thickness not greater than .014 of an inch andi having a .central :opening Athereim a series of bars spaced' about the periphconsisting of. iaminations;ot; thigh-permeability low cores-loss `-frriitgnetic material rotatably mounted within the stator, said rotor having its router surface spaced 'from the inner surface of the statorb'y axdi'stai'iee of not more than 5.00625 of an inch, saidroturlamixiations beingl insulated rom eachv otherwitht each of' said laminations .being of a thickness not Vgreaterthan .014 of an inch and having .'a series of bars uniformly spaced aboutits outer periphery withV conductor slots located .betweenV adjacent bars. the number Yery' of' said opening'with" conductor slotsllpcated "7' between the adjacent bars, the numberloi bars 1 said .series .being amulti'pleoi' four", alrtor of said bars. inv the rotor laminations being a multiple of four but notrlessy than eightand at least four less'than the number of. bars in the ,stator laininations, the bai-s irlV the. stator and the rotor having a per. unit'skewness equivalent to aper unitskewness. of vunity for the bars in ...the-retort n '6. 4In an alternating-current electromagnetic resolver. thercombiriation as dened in claim 5 wherein the stator and the rotor are one and ones-halfA inches.' ini length andthe rotor is 'one inch inidiameter.

'le In an ualternatingcurrent electromagnetic 4resolver, the .combination as defined-in claim 5 wherein the laminations for the stator and the rotor are formed from a magnetic material `consisting of from 47 to. 50 per cent nickeland identical distribution, of; their conductors inthe stator ccnductorslcts but with their' axes 0f electrical Y being spaced, mechanically v9i)iviegreesapart and apair ofmatched windings on the. x-fotor,V said rotor windings each' having an identical distribution of their conductors inV the rotor conductor slots but with their axes of electrical symmetry beingspaeed mechanically 90 degrees apart. f v

9.,y Iny van alternating-current2 electromagnetic resolver. the combination, that includes a stator ,and a rotor censistinggoff. laminations of a magnetic material,-f said; laminationsin the. (stator and the'rotor, respectively.. being insulated from each other and; consisting of from 47 to 50 per cent nickel and. 50 per cent iron, that. h as been hydrogen annealed each of the stator lamina,- tions having a. central opening therein, with a series of bars spaced about said opening with conductor slots, locatedbetfweei the adjacent bars,y the number ofpcle's in 'said seriesbeing rotor laminations being a. multiple off four but.

' resolveras defined in' claim 11y whereinthe stator notY less-"than eight f Tand' at least.'V four less than thev number f statonfbarsifsaidfrotor beingxrotatably. mountedv insidefof: the ,statorwith' the :faces of'v thev rotoribars; being-spaced `from the', faces aiies felectricalsyii'inety Ybeing spacedY 90 dei .grees apart. l' Y- Y l10.V In an alterhatingcu'rrent, electromagnetic resolver, vthe combination asdened in claim 9 whereinthere-areV twenty barsV in the stator and twelve bars in the rotor.

11'. An alternatingicurrent, electromagnetic resolver comprising .asta-tor, Aarotor rotatably mounted within therstzitor. said vstator. and rotor each being formed frcmlaminations of 'a high permeability, Vlcaw'sccreeloss magnetic. material and being notgieater than1g014 of an inch'thick,

said stator Y1ar'ninations'ffhaving 'twenty vbars spaced l.about theirinner periphery with conductor slots located' between" thefadjacentfbar's and said rotor laminations having twelve salient magnetic bars spaced about their outerfp'eriphery with conductor slots located .'between'- the ad jacent bars, said'stator'and'rotor b'a'rs having a peri unit skewnessv equivalent to a per unit. skewness. of unity" for'the rotr"bars-,; the. 'barpfaces of the stator bars being,v spaced front the bar faces of the rotor by a distance not" greater than .00625 of an inch. a pair cfimatched windings on the stator each of said stator windings having an identical distribution of conductors in conductor slots in the stator that are spaced mechanically degrees apart and a pair of matched windings on theV rotor each of said rotor windings having an identical'distribution of conductors inconductor slots-in the rotor that are spaced 90- degrees apart; Y

an ltematipsrevrrent.elgctremgeeii resolver as denedinclaim- 1l wherein thefstator and the rotor arefnot :greater- .than one. 'and one-half inches inv llngthlandthe motor ishn'ot 13. An alteriatin'gecurrent, electromagnetic resolver as dened in claim 11 wherein the stator and rotor laminations. are formed frozna hydrogen annealed magnetic material consisting of 47 to VV50 per cent nickel vancl'50 per cent pure n iron.

14. An alternating=current. electromagnetic and rotor are not greater than one and one-half inches in. lengtl'l` and the. Arotor isj not: more than onefinch in. diameter andv the stator VVand rotor laminations are formed from'afhydrcgen annealed magnetic material consisting'. of. from 47 to 50 per cent nickel and 50 per centpure iron.

I15. In analternatingcurrent electromagnetic, resolver,k the.l combination. that includes a. stator of laminated: magnetic materiali .ofhigh'permaability and low 'coreflossi `said stator: having` la central;y opening `'and a series; of barslunifcnnly spaced about'v its inner periphery with-.conductor slots` IQcated; `between the.: adiacent :bara the number: of saidibars. iin-saidseries being ai multiple of: fou-r; anal; ivmatehedrwindings carried by the: statortisaldwindinsfLha-vina an iden'- tical. distributipntofffconductorsgin conductor-slots of the stator that are spaced meclianinallgyi=H 9 0 T13 degrees apart, a lrotorfof .laminated magnetic material of high permeability and low core-l loss rotatably mounted within the stator, said rotor having a series ofv bar'suniformly spaced about itsA outer circumference with conductor 1 slots located between the adjacent bars, the number of said bars in said series being a multiple of four, but not less than eight and at least four less than the number of statorbars,

and a pair of matched windings carried by the` 16. In an electromagnetic resolver, the combination which includes a cylindrical housing, a stator of laminated magnetic material carried With said housing, an end bell engaging with and supporting the stator in a fixed position within the housing, a centrally disposed rotatable shaft located inside of said stator, said shaft being supported at one end by the end bell and at the other end by the housing, a rotor of laminated magnetic material rotatably supported within the stator on said shaft, said stator and rotor each having a series of spaced bars on their opposing surfaces with conductor slots located between the adjacent bars. the number of said bars on the stator and rotor being a multiple of four but being not less than twelve and eight respectively with the number of stator bars being at least four greater than the number of rotor bars, a pair of matched windings carried by the stator and a pair of matched windings carried by the rotor, each winding of the respective pairs of said windings having its axis of electrical symmetry spaced mechanically 90 degrees from the axis of electrical symmetry of the other winding of said pair.

17. In an electromagnetic resolver. the combination as deiined in claim 16 including contact rings carried by one end of the shaft supporting the rotor, said contact rings being insulated from each other and being respectively connected to the pair of matched rotor windings, a brush supporting ring of insulating material secured to the end bell and spring brushes carried by said brush supporting ring and contacting wtih said contact ring.

18. In an electromagnetic resolver. the combination as dened in claim 17 which includes a sector of an annular gear secured to and extending around a portion of the housing.

19. In an alternating-current electromagnetic resolver, the combination including a stator of laminated magnetic material, said stator having a central opening and a series of bars uniformly spaced about its inner periphery with conductor slots located between the adjacent bars, the number of stator bars in said series of bars being a multiple of four, a pair of matched windings on said stator, each of said windings having an identical conductordistributiondn conductor slots of the; stat'orit-hat are spaced mechanically 90 de- .grecs-apart,` a rotorof laminated magnetic material rotatably mounted-,within fthefzstator, said rotor having a series of .barsl uniformly spaced about its outer circumference with conductor slots located between the adjacent bars, the number of rotor bars in said series being a multiple of four, but not less than eight and at least four less than the, number of stator bars, a pair of matched windings on the rotor, each of said Iwindings having an identical conductor distribution in conductoi` slotsbf the `rotor that are spaced mechanically degrees apart and the bars-of the stator andgrotor are skewed with a per unit skewness equivalent toperl unit skewness of unity in the rotor bars.

20. In an alternating current electromagnetic resolver, the combination as dened in claim 19 wherein the conductors of each of the stator windings develop an alternating current fluxdensity distribution in the stator-rotor air-gap that'is sinusoidal in the angle of position on the stator periphery, fundamental in the space-period of the air-gap circumference and proportional to the alternating current voltage applied to the stator winding and the conductors of each of the rotor windings having induced in them a net alternating current voltage that is sinusoidal in the angle of rotor rotation with respect to the stator, fundamental in the space-period of the air-gap circumference and proportional to the alternating current voltage applied to either stator winding.

21. In an electromagnetic instrument of the character described, the combination as dened in claim 1 which includes a pair of matched windings having conductors located in the conductor slots oi' the stator, said stator windings having their axes of electrical symmetry spacedapart mechanically by 90 degrees, a pair of matched windings having conductors located in the conductor slots of the rotor, said rotor windings having their axes of electrical symmetry spaced apart mechanically by 90 degrees, each of said stator and rotor windings having a conductor distribution which is identical in all four quadrants of the magnetic structure of the stator and rotor, respectively, with the conductors of each winding being located in all of said conductor slots except the conductor slots located at 90 and 270 degrees with respect to the zero axis of the respective winding and the distribution of the conductors of each winding among the conductor slots of each quadrant in which conductors of said winding are present is chosen to eliminate the maximum number of space-harmonics above the rst.

22. In an electromagnetic instrument of the character described, the combination :as dened in claim 1 which includes a pair of matched windings having conductors located in the conductor slots of the stator, said stator windings having their axes of electrical symmetry spaced apart mechanically by 90 degrees, a pair of matched windings having conductors located in the conductor slots of the rotor, said rotor windings having their axes of electrical symmetry spaced apart mechanically by 90 degrees, each of said statorI and rotor windings having a conductor distribution which is identical in all four quadrants of the magnetic structure of the stator and rotor, respectively, with the conductors of each winding being located in all of said conductor slots except the conductor slots located at 90 and 270 degrees with respect to the zero axis of the respective winding and the cistributon of'conductofsof each winding among "$608,652 Y Y l5 ..16

Y "j: REFERENCES CITED` l y K the conductor 51.0135 ai each quadxant'mwmch 1 The'foldwing refrence yare of recbd 'the conductors of salut; vu1r1d1ng-'-mze.rmesent s'chosen 'me @this ptenu Y 1 l v to' eliminate the maxmumnumberof. Space-har'- 1 monies eulocsvetheI rstin theformula v 5 Numbr *Namfe- DateL-J: 

